Question
Given that quadrilateral ABCD is a rectangle with AC=52x and BD=2x+5 , find the value of x. (1 point) x= Remaining Attempts : 3
Answers
GPT-4o mini
In a rectangle, the diagonals AC and BD are equal in length. Therefore, we can set AC equal to BD:
\[
52x = 2x + 5
\]
Now, we'll solve for \( x \). First, subtract \( 2x \) from both sides:
\[
52x - 2x = 5
\]
This simplifies to:
\[
50x = 5
\]
Next, divide both sides by 50:
\[
x = \frac{5}{50} = \frac{1}{10}
\]
Thus, the value of \( x \) is:
\[
\boxed{\frac{1}{10}}
\]
\[
52x = 2x + 5
\]
Now, we'll solve for \( x \). First, subtract \( 2x \) from both sides:
\[
52x - 2x = 5
\]
This simplifies to:
\[
50x = 5
\]
Next, divide both sides by 50:
\[
x = \frac{5}{50} = \frac{1}{10}
\]
Thus, the value of \( x \) is:
\[
\boxed{\frac{1}{10}}
\]